MRI pulse shaping using inverse scattering and optimization

Most magnetic resonance imaging (MRI) sequences employ field gradients and radio-frequency (rf) selective pulses to excite only those spins lying in a specific plane. The fidelity of the resulting magnetization distribution is crucial to overall image resolution. Due to the nonlinear relationship between a pulse envelope and its resultant magnetization distribution, there is no simple inversion formula to guide the design of selective rf pulses. Conventional rf pulse design techniques rely on the small tip-angle approximation to Bloch equations, which is inadequate for the design of 90{dollar}spcirc{dollar} and 180{dollar}spcirc{dollar} pulses. Recently, some researchers have reformulated the inverse Bloch transform problem as a two-component wave system inverse scattering problem of Zakharov-Shabat type. This thesis considers fast algorithms for solving these inverse scattering problems. Computer simulations show some of these results need improvements.; To address the deficiencies, an alternative optimization approach is developed. The full nonlinear Bloch equations are used and the pulse shapes are obtained by minimizing a measure of departure from the desired magnetization distribution. Solutions generated by the scattering problem approach provide good pulse shapes for starting the descent algorithms which are used in the optimization process. The optimized pulse shapes have a highly oscillatory behavior, which are successfully smoothed by adding a regularization term to the cost function. A variety of novel selective pulses are successfully developed. These pulses have been practically implemented on a commercial NMR imager and experimental results agree with the simulation results. The regularized formulation of the optimization technique is further applied to the design of two-dimensional (2D) spatially selective inverting pulses. The designed 2D inverting pulses have a maximum gradient slew rate about 3 times higher than the targeted hardware limit (2000G{dollar}cmsp{lcub}-1{rcub} ssp{lcub}-1{rcub}{dollar}) and the resultant {dollar}Msb{lcub}z{rcub}{dollar} profiles have only a few small ripples. Increases in slice thickness seem to be a consequence of lower gradient slew rates.